Finite Group DatabasebetaFinite Group Databasebeta| order | 15616 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C61 · Schur multiplier (H2) = C23 |
| direct product | C61×#12951 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C61 | #476 |
| commutator | C2×C8 | C22×C4×C61 |
| Frattini, cosocle | C22×C8 | C23×C61 |
| socle | C2×C61 | #1864 |
| prime radical | C2×#135×C61 | C22 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C61 ◁ C22×C4×C61 ◁ C2×C4×C8×C61 ◁ G | |
406 conjugacy classes of subgroups.
| minimal degree | μ(G) = 93 |
| transitive degree | μt(G) = 1952 |
A minimal faithful permutation representation — 3 generators on 93 points:
(1,2,6,13,8,14,7,26)(3,15,18,27,20,31,19,30)(4,21,5,24,23,12,22,11)(9,17,28,16,29,32,10,25)(33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93);(1,3)(2,9,14,29)(4,17)(5,25)(6,19)(7,18)(8,20)(10,26,28,13)(11,27,24,30)(12,31,21,15)(16,22)(23,32);(1,3)(2,10)(4,17)(5,25)(6,19)(7,18)(8,20)(9,26)(11,15)(12,27)(13,29)(14,28)(16,22)(21,30)(23,32)(24,31)2806 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15616, 5939);